2019/12/04 by Nikola Sandrić, Sandrić, Nikola, Ivana Valentić +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1912.02082
openalex publication_date 2019/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we consider the problem of periodic homogenization of a Feller process generated by a pseudo-differential operator, the so-called Lévy-type process. Under the assumptions that the generator has rapidly periodically oscillating coefficients, and that it admits "small jumps" only (that is, the jump kernel has finite second moment), we prove that the appropriately centered and scaled process converges weakly to a Brownian motion with covariance matrix given in terms of the coefficients of the generator. The presented results generalize the classical and well-known results related to periodic homogenization of a diffusion process.